Abstract: In this paper, we investigate the a.s. asymptotic behaviour of the solution of the stochastic differential equation , where and are positive continuous functions and is a standard Wiener process. By an application of the theory of PRV and PMPV functions, we find conditions on and , under which may be approximated a.s. on by the solution of the deterministic differential equation . Moreover, we study the asymptotic stability with respect to initial conditions of solutions of the above SDE as well as the asymptotic behaviour of generalized renewal processes connected with this SDE.